1D Cut List Optimizer

How to use the 1D Cut List Optimizer

1. Pick a unit system. Millimeters for metric shops, inches for imperial. The toggle converts existing values so you don't have to retype.
2. Enter the stock length. The length of bars, pipes or cables you buy from the supplier — 6000 mm structural steel, 20 ft conduit, a 100 m cable spool.
3. Set the kerf. How much material the blade or shear removes per cut. Typical values: 3 mm for a wood blade, 1.5 mm for a thin metal-cutting disc, ~0 for cable shears.
4. List the cuts. One row per required piece length, with quantity. Add as many rows as you need. The default shows 2× 1200 mm and 5× 800 mm as an example.
5. Read the plan. Each bar is drawn as a colored strip with the pieces in proportion and the unused stub at the right. The cuts inside each bar are listed in cutting order — descending — so the list reads top to bottom the way you'd cut on the saw.

What is 1D cutting optimization?

The cutting stock problem: given a stock length and a list of shorter pieces, find the layout that uses the fewest bars. It's a classic combinatorial optimization problem — exact solutions are NP-hard, but fast heuristics get within a few percent of optimal for everyday cut lists. This calculator uses First-Fit Decreasing, the standard heuristic, with a proven worst case of 11/9 the optimal number of bars.

1. Sort all pieces from longest to shortest.
2. For each piece, scan existing bars left to right
   and drop it into the first one with room
   (room = stock_length − used − kerf).
3. If no bar fits, start a new bar.

The kerf — the slice of material the saw removes with every cut — is added between every pair of consecutive pieces in the same bar. Ignoring it is the most common reason a cut list "fits on paper" but leaves the last piece a few millimeters short.

Examples

• Steel I-beam shop: 12 m stock, 3 mm kerf, six pieces — 2× 4 m, 4× 1.8 m. Plan: one bar fits 4 m + 4 m + 1.8 m (with kerfs) = 9806 mm, second bar fits 3× 1.8 m = 5406 mm. Two bars, ~63% efficiency.
• Aluminum window profile: 6 m stock, 1.5 mm kerf, cut list for two sashes — 4× 1.2 m and 4× 0.8 m. Plan: each bar handles a complete sash with minimal offcut. Two bars, ~67% efficiency.
• Electrical conduit: 3 m stock, 0 mm kerf (clean cable shear), pulling lengths — 10× 0.5 m, 5× 1 m, 2× 1.5 m. The optimizer fills four bars cleanly with very little waste.

FAQ

What is a 1D cut list optimizer?

A tool that takes a stock length, a list of required cut pieces and a saw kerf, and returns a cutting plan that fits the pieces into as few bars as possible. "1D" because it only cares about length — sheet materials need a 2D optimizer instead. Common users are carpenters, metalworkers, plumbers, electricians and aluminum-window shops.

What is the saw kerf and why does it matter?

Kerf is the slice of material the blade or shear destroys with every cut. A circular saw is about 3 mm, a thin metal-cutting disc 1.5 mm, a cable shear is essentially zero. Ignoring kerf means your pieces end up a few millimeters short and your last cut may not fit.

Is the result the absolute optimum?

It is a strong near-optimum using First-Fit Decreasing — pieces are sorted largest first, then packed into the next bar that has room. FFD is mathematically proven to use at most 11/9 of the optimal number of bars and is the standard heuristic for the cutting stock problem. For everyday cut lists the result is usually optimal.

What materials is this suitable for?

Anything sold in linear stock: timber, plywood strips, steel and aluminum bars, square and round tube, electrical conduit, copper pipe, cable runs, MDF strips, window and door profiles, fence panels. If it comes in a length and you cut it shorter, the calculator works.

How do I read the bar visualization?

Each bar is drawn as a horizontal strip. Coloured segments are your pieces in proportion to their length. The striped grey segment at the end is the unused stub left after the cuts. The percentage is how much of the bar you actually used.

Why is one of my bars almost empty?

You have leftover pieces that did not fit alongside the others. To reduce that waste, try adjusting your piece sizes if you have flexibility (e.g. ordering 2.4 m instead of 2.5 m), choosing a different stock length, or seeing whether the leftover piece can be re-used elsewhere.

Privacy

Every calculation runs in your browser. Your cut list and dimensions never leave your device — nothing is sent to a server, nothing is stored in cookies, nothing is logged. The only thing this site remembers is whether you prefer millimeters or inches, kept locally so you don't have to toggle it every visit.